The slope of the line represented by the equation -5x + 2y = 10 is slope = -5/2 and y intercept= -5
In order to answer the question, we must first simplify the given linear equation so that it may be expressed as a regular linear equation with slope and intercept. A linear equation's slope intercept form is y=mx+b , where "m" denotes the line's slope and "b" its y-intercept. The value of y = 0 must then be entered for the x-intercept, and the value of "x" must then be determined. We will obtain all necessary values in this manner.
By slope-intercept form equation of the line:
y=mx+b
The advantage of the equation in this form is that m and b can be derived 'easily'
Rearrange -5x-2y = 10 in this form.
-2y=5x+10
y=-5/2x+-10/2
y=-5/2x-5
slope = -5/2
y intercept= -5
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13. The table shows the prices of several types of rice.
Thomas purchases 1.25 pounds of white long
grain rice and 2.25 pounds of brown jasmine rice.
If Thomas pays for his purchase with a $20 bill,
how much will he receive in change? Round the
answer to the nearest cent.
Rice
White Long Grain
White Basmati
Brown Jasmine
Cost (per lb)
$0.70
$1.85
$2.10
1.
2
HOW IS THE ANSWER HELP PLEASE✋
Hence the change that Jasmine is going to receive from the expenditure on the rice is $14.4
How to solve for the changeThe price of the white long grain rice = 0.70 dollars
The price of the brown jasmine rice is 2.10 dollars
The quantity that was bought from each is 1.25 and 2.25
Hence we would have the total expenses as
0.70 dollars x 1.25 and
2.10 dollars x 2.25
= 0.875 + 4.725
= 5.6 dollars
Hence the total expenditure that Jasmine has done is 5.6 dollars. The difference would be the change that he would receive.
= $20 - $5.6
= $14.4
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he altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. what is the area of the triangle, in square units? express your answer in simplest radical form.
The area of the triangle is 6√3 square units.
What is the hypotenuse of a triangle?A triangle with a right angle or two perpendicular sides is referred to as a right triangle, a right-angled triangle, or perhaps more formally as an orthogonal triangle (formerly known as a rectangle triangle). Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
According to the given data:The ratios of a given object's sides 30°-60°-90° triangle are 1 : √3: 2.This information allows us to calculate the lengths of something like the triangle's orthogonal sides.
3(2/√3) = 2√3 . . . . side AB in the attached figure.
And also:
2·3 = 6 . . . . . . . . . . side AC in the attached figure.
Then the area of the triangle is:
A = 1/2bh
A = 1/2(6)(2√3) = 6√3 . . . . square units.
the area of the triangle 6√3 square units.
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Find the average rate F(x)=7x-12 from -2 to 3
The average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.
As given in the question,
Given function F(x) = 7x -12
x₁= -2
x₂ =3
Average rate of the function F(x) is
= {F(x₂) - F(x₁)}/ (x₂ - x₁)
= [7(3)-12 - {7(-2)-12}]/ [3-(-2)]
=(21-12+14+12)/ 5
=35/5
=7
Therefore, the average rate of given function F(x) = 7x -12 from -2 to 3 is equal to 7.
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- Find BC if B(8, -7) and C(-4, -2).
The line segment BC has a length of 13 units.
What is the length of a line segment?
In this question we know the locations of the two ends of a line segment. The procedure consists in calculating the vector behind the line segment and later determing its magnitude by Pythagorean theorem. If we know that B(x, y) = (8, - 7) and C(x, y) = (- 4, - 2), then the length of the line segment BC is:
BC = (- 4, - 2) - (8, - 7)
BC = (- 12, 5)
BC = √[(- 12)² + 5²]
BC = 13
The line segment BC has a length of 13 units.
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If p < 0, q > 0, and p + q = r, which statement about r is true? A number line shows p to the left of 0 and q to the right of 0, with q closer to 0 than p. |r| = |q| r > 0 r < 0 |r| > |q|
The correct option is r < 0 for the given inequalities of p < 0, q > 0, and p + q = r.
What is defined by the number line?You can select any point as "0," and all positive numbers will be to the right of the "0," and all negative numbers will be to the left of the "0." A line of infinite length, the points of which correspond to real numbers based on their distance in a negative or positive position from a point randomly chosen as zero.A number line is a straight line to numbers at equal intervals or sections along its length. A number line could be extended in any direction indefinitely and is typically represented horizontally.For the given inequalities;
p < 0, q > 0, and p + q = r;
As, we know that if p < 0; then it hold the negative value.
And for q > 0, it have the positive values.
Because -negative(P) was closer to zero than Positive q, let's say p = -10 and q = 5.
p + q = r
Put the values;
r = -10 + 5 = -5,
r = -5
Therefore, r < 0 is the correct condition for the given inequalities.
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34 - 2x = 3x + 4 what is the answer with the work
Find the value of x.
(4x+8) =
Answer:
Step-by-step explanation:
(4x+8)
4(x+2)
Help please thank you
Answer: itll be 2/3 im pretty sure
Step-by-step explanation:
please give a detailed explanation
Answer:
1) Constant
2) Decreasing
3) Increasing
Step-by-step explanation:
1) Graphically, we can say that a function is constant if we see a flat line, which means that the range is the same throughout its domain, in this case we have one flat line, therefore it is a constant function
2) The graph is going down as it moves from left to right in all the domain, that means it's decreasing
3) The graph is going up as it moves from left to right in all the domain, that means it's increasing.
Solve the "or" inequality
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a x ≥2 or x ≤ -2.
According to the statement
We have to find that the value in the inequality.
So, For this purpose, we know that the
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
From the given information:
7x-14 ≥0 or 4x+5 ≤ -3
The value of the inequality is a :
7x-14 ≥0 or 4x+5 ≤ -3
x ≥14/7 or x ≤ -3-5/4
x ≥2 or x ≤ -8/4
x ≥2 or x ≤ -2.
So, The value of the inequality is a x ≥2 or x ≤ -2.
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Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, approximately how many inches are in 1 km?
Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
From the problem, the conversion factors are given as
1 kilometer = 0.62 mile
36 inches = 1 yard
1 mile = 1760 yards
To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile
1 km = 0.62 miles
Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards
1 km = 0.62 miles = 0.62 (1760 yards)
1 km = 0.62 miles = 1091.2 yards
Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard
1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)
1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches
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7) Danice went to the grocery store and purchased 3 packets of noodles, 5 packets of cookies, and 2 packets of dry fruits. If the cost of each packet of noodles, cookies, and dry fruits is $2. $20 and 50 respectively. What is the total amount paid by Danice?
Answer: $206
Step-by-step explanation:
n=packets of noodles.
c=packets of cookies.
d=packets of dry fruit.
2n+20c+50d=
2(3)+20(5)+50(2)=
6+100+100=
6+200=$206
we both play a game where we flip a coin. you win if 3 heads appear, i win if 3 tails appear. what is the expected number of flips for the game to end.
Answer:
9
Step-by-step explanation:
9 because 3x3=9
A die is rolled twice.
What is the probability of rolling a 3 followed by a 2?
chance of 3 is 1/6 and chance of 2 is 1/6 so finale answer is 1/36
I’m thinking of a number when I add 1 and then take 2/3 of it I get 18 what is my number
Answer:
53/3
Step-by-step explanation:
[tex]x \: + 1 - \frac{2}{3} = 18 \\ x \: - \frac{2}{3} = 18 - 1 \\ x - \frac{2}{3} = 17 \\ x = \frac{17}{1} + \frac{2}{3} \\ x = \frac{51 + 2}{3} \\ x = \frac{53}{3} \\ check \\ \frac{53}{3} + \frac{1}{1} \\ = \frac{53 + 3}{3} \\ = \frac{56}{3} - \frac{2}{3} \\ = \frac{56 - 2}{3} \\ x = \frac{54}{3} \\ x \: = 18[/tex]
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12.5% complete question a painting crew reported that a job is 35 completed. what fraction of the job remains to be done?
Answer:
13/20
Step-by-step explanation:
I hope this helps, have a great day :)
Carter wants to ride his bicycle 28.7 miles this week. He has already ridden 17 miles. If he rides for 3 more days, write and solve an equation which can be used to determine mm, the average number of miles he would have to ride each day to meet his goal.
The equation which can be used to solve the the average number of miles he would have to ride to meet his target is 28.7 = 17 + 3x.
The solve equation is x = 3.9 miles.
How to find the number of miles he will ride each day with an equation?He wants to ride his bicycle 28.7 miles this week.
He has already ridden 17 miles.
He rides for 3 more days.
The equation which can be used to determine the average number of miles he would have to ride to meet his target can be calculated as follows:
The total distance to ride is 28.7 miles.
Therefore,
28.7 = 17 + 3x
where
x = number of miles he will travel for the remaining 3 daysTherefore,
28.7 = 17 + 3x
subtract 17 from both sides of the equation
28.7 = 17 + 3x
28.7 - 17 = 17 - 17 + 3x
11.7 = 3x
divide both sides by 3
3x / 3 = 11.7 / 3
x = 11.7 /3
x = 3.9
Therefore, he needs to travels 3.9 miles daily for 3 days.
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What is the sum of the following numbers?
-7, 5, -3, 6, -4, 7, -5, 3, -1, 4
Answer:
5
Tips to Add Negative and Positive Numbers:
1.) Adding a negative number to a positive number is subtracting it.
example: 5 + (-3) = 5 - 3
2.) Adding a positive number to a smaller negative number is subtracting the smaller number by the larger one.
example: -3 + 5 = 5 - 3
3.) Adding a positive number to a larger negative number is having the positive number subtracted by the larger negative.
example: -5 + 3 = 3 - 5 (but the final answer needs a negative sign)
4.) Adding a negative number to another negative number is adding the numbers together, but with a negative sign in the final calculation.
example: -3 + (-2) = 3 + 2 (but the final answer needs a negative sign)
5.) I think you know how to add two positive numbers
(I know the wording of the tips can be confusing, so make sure to look at the examples if you don't understand)
Class work help Algebra 2
Answer:Algebra 2 is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.
[tex]\frac{x}{2}=\frac{4}{x} -1[/tex]
[tex]\fbox{x = - 4} \: \sf or \: \fbox{ x = 2}[/tex]
Step-by-step explanation:
[tex] \frac{x}{2} = \frac{4}{x} - 1[/tex]
multiply whole equation with 2x,
[tex] \hookrightarrow\frac{x}{2} \times 2x = ( \frac{4}{x} \times 2x) - (1 \times 2x)[/tex]
[tex]\hookrightarrow {x}^{2} = 8 - 2x[/tex]
Rearranging above equation and making a quadratic equation,
[tex]\hookrightarrow {x}^{2} + 2x - 8 = 0[/tex]
Comparing above equation with, ax²+bx+c,
a =1, b=2, c= -8
Using formula,
[tex]x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
Substituting the given values,
[tex]x = \frac{ - 2 ± \sqrt{ {2}^{2} - 4 \times 1 \times ( - 8)} }{2 \times 1}[/tex]
[tex]x = \frac{ - 2 ± \sqrt{ 4+32} }{2}[/tex]
[tex]x = \frac{ - 2 ± 6 }{2}[/tex]
[tex]x = \frac{ - 2 + 6}{2} = \frac{4}{2} = 2[/tex]
or
[tex]x = \frac{ - 2 - 6}{2} = \frac{ -8}{2} = - 4[/tex]
[tex] \fbox{x = -4} \: \sf or \: \fbox{ x = 2}[/tex]
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Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
0. 61
61/100 is the equivalent fraction for the given decimal number.
A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point.
A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection.
for converting a decimal into a fraction we need to multiply and divide the decimal by the 10^n where n is the number of digits after the decimal.
61/100 is the equivalent fraction for the given decimal number.
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Mr. Johnston supports a young tree by using a stake and a string forming a right angle with the ground.
60 in.
33 in.
What is the length of the string? Round to the nearest tenth.
Answer:68.48
Step-by-step explanation:a²+b²=c² a=60 b=33 so 60²+33²=4689 and take the square root of that which equals 68.48
classify the following data. indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. the amount of time each of five randomly selected basketball players play during a game.
The given data is quantitative, continuous, ratio.
What is qualitative data?
Quantitative data is information that is expressed as counts or numbers, each of which has a specific numerical value. Data is any measurable information that may be used by academics for statistical analysis and mathematical computations so that they can derive practical conclusions.
Quantitative information provides answers to inquiries like "How many?," "How often?," and "How much?" Mathematical approaches may be used to easily verify and assess this data.
What is continuous and ratio data?
If a continuous variable has a meaningful zero point, it is regarded as a ratio (i.e., as in age or distance).
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A square pyramid has a base with a side length of 6 meters. If the
slant height of the pyramid is 5 meters, what is the surface area of the
pyramid?
m²
Answer:
96
Step-by-step explanation:
?
The surface area of the square pyramid with length of the base 6m and slant height of the pyramid 5m is 96 m².
A square pyramid is a 3-D geometrical figure with the base of the shape of square and four triangular faces from each side of the square joining together at the top to form vertex.
The surface area of a square pyramid is given as:
Base area of the square face + 1/2 (perimeter of base × slant height)
Since square base has side of length 6m and the slant height of the pyramid is 5m then surface area is given by;
Surface area = (6×6) + 1/2 (4×6×5)
=> 36 + 1/2 (120)
=> 36 + 60
=> 96 m²
Thus, surface area of square pyramid is 96 m².
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3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10
Answer:
z = -4
Step-by-step explanation:
Let's solve the problem,
→ 3(z - 1) - 1/2 (4z + 10) = 4 (z - 3/2) + 10
→ 3z - 3 - 2z - 5 = 4z - 6 + 10
→ z - 8 = 4z + 4
→ 4z - z = -4 - 8
→ 3z = -12
→ z = -12/3
→ [ z = -4 ]
Hence, the value of z is -4.
A linear function is shown on the graph.
a linear function beginning with closed circle at 0 comma 2 and ending with a closed circle at 4 comma 6
What is the domain of the function?
{x | 0 ≤ x ≤ 4}
{x | 0 < x < 4}
{y | 2 ≤ y ≤ 6}
{y | 2 < y < 6}
Answer:
A) {x | 0 ≤ x ≤ 4}Step-by-step explanation:
The x-coordinates form the domain.
We know the x-coordinates of the end points of the line, the first numbers in pair of coordinates:
x = 0 and x = 4Also, since both points are closed circles, the endpoints are included.
So the domain is the interval between 0 and 4, both inclusive.
This is shown as:
{x | 0 ≤ x ≤ 4}The matching answer choice is A.
The domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, the function begins with a closed circle at (0, 2) and ends with a closed circle at (4, 6), which means that the function is defined at these specific points.
Since the function is a linear function, it represents a straight line.
A linear function is continuous, and it extends indefinitely in both directions.
Therefore, any x-value between 0 and 4 will also be defined by the linear function.
In mathematical notation, we can represent the domain as:
Domain: {x | 0 ≤ x ≤ 4}
This means that the domain of the function includes all x-values from 0 to 4, including both 0 and 4.
So, the correct answer is option A: {[tex]{x | 0 \leq x \leq 4}\\[/tex]}.
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complete question:
A linear function is shown on the graph.
a linear function that passes through the points (0, 2) and (4, 6)
What is the domain of the function?
[tex]{x | 0 \leq x \leq 4}\\{x | 0 < x < 4}\\{y | 2 \leq y \leq 6}\\{y | 2 < y < 6}[/tex]
graph is attached
Which is 3 groups of 5?
3 + 5
5 - 3
3 × 5
5 ÷ 3
Answer: 3 groups of 5 = 5 + 5 + 5 = 15. 5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15. 3 groups of 5 has the same answer as 5 groups of 3! So, 3 x 5 = 5 x 3. This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same. Multiplication Terms
Step-by-step explanation: I hopes this helps.
write the index notation of 3*3*3*3
Answer:
[tex]3^{4}[/tex]
Step-by-step explanation:
Because 3x3x3x3
3 multipily by 4 times as it's same number
An elevator can carry 15 adults or 20 children at one time during the course of a day the elevator Carries a full passenger load 52 times if all the passengers were children how many more people would the elevator carry than If all the passengers were adults
An elevator can carry 15 adults or 20 children at one time during the course of a day the elevator Carries a full passenger load 52 times if all the passengers were children 260 more people would the elevator carry than If all the passengers were adults.
52 trips[tex]\times[/tex]15 adults = 780 adults for the course of a day
52 trips[tex]\times[/tex] 20 children = 1,040 children for the course of a day
The elevator can carry 1040-780=260 more children than adults in a day
A vehicle that travels in a vertical shaft to transport people or cargo between floors of a multistory structure is an elevator, also known as a lift. The majority of contemporary elevators are moved by electric motors through a network of wires and sheaves with the help of a counterweight (pulleys).
Traction elevators come in two varieties: gearless traction and gearless traction. The most sophisticated option is a gearless traction elevator, which operates the hoisting mechanism using counterweights and has a wheel that is directly connected to the engine.
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The figure to the right shows the graph y= 3^-x and three inscribed rectangles. What is the sum of the areas of the rectangles?
Based on the calculations, the sum of the areas of the rectangles is equal to: A. 0.25 square unit.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.By critically observing the figure (see attachment), we can logically deduce the following information:
Width of rectangle A = 2 units
Width of rectangle B = 2 units.
Width of rectangle C = 4 units.
Next, we would determine the length and area of each of the rectangle.
The length of the first rectangle is given by:
Length of rectangle, y = 3^-x
Length of rectangle, y(0) = 3⁻⁰ = 1 units.
Length of rectangle, y = 3^-x
Length of rectangle, y(2) = 3⁻² = 0.11 unit.
Area of first rectangle = 2(0.11)
Area of first rectangle = 0.22 square unit.
For the second rectangle, we have:
Length of second rectangle, y = 3^-x
Length of second rectangle, y(4) = 3⁻⁴ = 0.012 unit.
Area of second rectangle = 2(0.012)
Area of second rectangle = 0.025 square unit.
For the third rectangle, we have:
Length of third rectangle, y = 3^-x
Length of third rectangle, y(8) = 3⁻⁸ = 0.00015 unit.
Area of third rectangle = 4(0.00015)
Area of third rectangle = 0.0006 square unit.
Now, we can calculate the sum of the areas of the rectangles:
Total area = 0.22 square unit + 0.025 square unit + 0.0006 square unit.
Total area = 0.246 ≈ 0.25 square unit.
Total area of rectangle = 0.25 square unit.
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Complete Question:
Figure 3 shows the graph of y = 3^−x and three inscribed rectangles. What is the sum of the areas of the rectangles?
[a] 0.25
[b] 0.50
[c] 2.45
[d] 6.26
[e] 12.68